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A suitable approach to this question involves analyzing the position-time graph in order to develop a verbal description of the moving object it represents. Then match the verbal description to the particular features of a velocity-time graph would be consistent with such a motion.
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The position-time graph displays a straight diagonal line with negative slope. The negative slope represents an object with a negative velocity. The straightness of the line represents an object that is moving with a constant velocity. Thus, the graph represents a motion with a constant negative velocity.
A constant velocity on a velocity-time graph is represented by a horizontal line. A negative velocity on a velocity-time graph is represented by a line located in the negative region of the graph (below the time axis).
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Velocity-Time Graphs:
Velocity versus time graphs represent changes that occur in an object's velocity with respect to time. These graphs most commonly display horizontal lines or straight diagonal lines. Horizontal lines represent an object with a constant velocity. If the horizontal line is on the time axis, the object is at rest (a constant velocity of 0 m/s). If the horizontal line is above or below the time axis, then the object is moving with a constant positive or a constant negative velocity. Straight diagonal lines represent an accelerated motion. The slope of the line is the acceleration of the object.
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Position-Time Graphs:
Position versus time graphs represent changes that occur in an object's position with respect to time. These graphs most commonly display horizontal lines, straight diagonal lines and curved lines. Horizontal lines represent an object at rest. Straight diagonal lines represent a constant speed motion. Curved lines represent an accelerated motion. The slope of the line is the velocity of the object. Steeply-sloped lines represent fast-moving objects. Gently-sloped lines represent slow-moving objects.
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